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A method of solving combinatorial problems by means of an algorithm which is allowed to run forward until a dead end is reached, at which point previous steps are retraced ...

A binary plot of an integer sequence is a plot of the binary representations of successive terms where each term is represented as a column of bits with 1s colored black and ...

A circular pattern obtained by superposing parallel equally spaced lines on a set of concentric circles of increasing radii, then coloring the regions in chessboard fashion. ...

Given any assignment of n-element sets to the n^2 locations of a square n×n array, is it always possible to find a partial Latin square? The fact that such a partial Latin ...

The maximum possible weight of a fractional clique of a graph G is called the fractional clique number of G, denoted omega^*(G) (Godsil and Royle 2001, pp. 136-137) or ...

The König-Egeváry theorem, sometimes simply called König's theorem, asserts that the matching number (i.e., size of a maximum independent edge set) is equal to the vertex ...

Beautiful patterns can be created by drawing sets of nested polygons such that the incircle of the nth polygon is the circumcircle of the (n+1)st and successive polygons are ...

Ramsey's theorem is a generalization of Dilworth's lemma which states for each pair of positive integers k and l there exists an integer R(k,l) (known as the Ramsey number) ...

The average number of regions N(n) into which n lines divide a square is N^_(n)=1/(16)n(n-1)pi+n+1 (Santaló 1976; Finch 2003, p. 481). The maximum number of sequences is ...

The Szilassi polyhedron is a heptahedron that is topologically equivalent to a torus and for which every pair of faces has a polygon edge in common. The Szilassi polyhedron ...